Compound Poisson Approximation

Compound Poisson Approximation appears naturally in situations where one deals with a large number of rare events. It has important applications in insurance, extreme value theory, reliability theory, mathematical biology, etc. This book synthesizes the most important recent research in the field in a single volume.

Compound Poisson approximation appears naturally in situations where one deals with a large number of rare events. It has important applications in insurance, extreme value theory, reliability theory, mathematical biology, and more. Compound Poisson Approximation synthesizes the most important recent research in the field in a single volume. With an extensive list of references, open problems, and exercises, it will become the standard reference book on the topic.

Features

• Provides a comprehensive overview of this rapidly expanding field

• Synthesizes the most important research results of recent years

• Presents an array of special topics

• Provides the reader with a set of tools needed for research and education

The book is of interest to researchers and postgraduate students from probability, statistics, and mathematics.

Autorentext

Vydas ekanaviius is a Professor of Mathematics at the Institute of Applied Mathematics, Faculty of Mathematics and Informatics, Vilnius University. He is the author of Approximation Methods in Probability Theory, Springer, 2016.

Dr S.Y. Novak works at Middlesex University London. He is the author of Extreme value methods with applications to finance, Chapman & Hall/CRC Press, 2011.

Klappentext

Compound Poisson Approximation appears naturally in situations where one deals with a large number of rare events. It has important applications in insurance, extreme value theory, reliability theory, mathematical biology, etc. This book synthesizes the most important recent research in the field in a single volume.

Inhalt

1. Preliminaries. 2. Poisson limit theorem. 3. Accuracy of Poisson approximation. 4. Applications. 5. Compound Poisson limit theorem. 6. Accuracy of CP approximation: rare events. 7. Accuracy of CP approximation: discrete r.v.s. 8. Special classes of distributions. 9. m-dependent integer-valued r.v.s.
2. Markov Binomial distribution. 11. Multivariate compound Poisson approximation. 12. Compound Poisson process approximation. 13. Kolmogorov's problem. 14. Appendix.